Quadratic formula -rocket height at given equation

Question

A rocket's height is $190$ m that is defined by an equation $c^2 + 160c +20$. What will the equation be when the rocket's height is $60$ m?

Can anyone give me some clue in solving the above problem?

Answer 1

STRONG HINT:

We must do $\frac{190}{60}$ which simplified equals $\frac{19}{6} \implies \frac{190}{19/6} = \frac{6 \times 190}{19} = 60$.

$$\therefore \frac{6(c^2 + 160c + 20)}{19} \ \ \text{determines the height of the rocket at 60m}$$ $$\begin{align} &= \frac{6c^2 + 960c + 120}{19} \\ &= \frac{6}{19}c^2 + \frac{960}{19}c + \frac{120}{19} \end{align}$$ Now use the formula: $$x = \left\{\frac{-b \pm \sqrt {\Delta}}{2a} : \Delta = \text{discriminant}, b^2 - 4ac\right\}$$ And you will find the value for $c$. To calculate the time the rocket will take to travel $60$m high, we use the formula:

$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$

$\because c =$ Time and $60 =$ Distance, you can calculate the speed.